Renormalized perturbation theory: Vlasov–Poisson system, weak turbulence limit, and gyrokinetics

The self-consistency of the renormalized perturbation theory of Zhang and Mahajan [Phys. Rev. 132, 1759 (1985)] is demonstrated by applying it to the Vlasov–Poisson system and showing that the theory has the correct weak turbulence limit. Energy conservation is proved to arbitrary high order for the electrostatic drift waves. The theory is applied to derive renormalized equations for a low-beta gyrokinetic system. Comparison of this theory with other current theories is presented.